8,843 research outputs found

### Perturbative Confinement

A Procedure is outlined that may be used as a starting point for a
perturbative treatment of theories with permanent confinement. By using a
counter term in the Lagrangian that renormalizes the infrared divergence in the
Coulomb potential, it is achieved that the perturbation expansion at a finite
value of the strong coupling constant may yield reasonably accurate properties
of hadrons, and an expression for the string constant as a function of the QCD
Lambda parameter.Comment: Presented at QCD'02, Montpellier, July 2002. 12 pages LaTeX, 8
Figures PostScript, uses gthstyle.sty Reprt-no: ITF-2002/39; SPIN-2002/2

### TransPlanckian Particles and the Quantization of Time

Trans-Planckian particles are elementary particles accelerated such that
their energies surpass the Planck value. There are several reasons to believe
that trans-Planckian particles do not represent independent degrees of freedom
in Hilbert space, but they are controlled by the cis-Planckian particles. A way
to learn more about the mechanisms at work here, is to study black hole
horizons, starting from the scattering matrix Ansatz.
By compactifying one of the three physical spacial dimensions, the scattering
matrix Ansatz can be exploited more efficiently than before. The algebra of
operators on a black hole horizon allows for a few distinct representations. It
is found that this horizon can be seen as being built up from string bits with
unit lengths, each of which being described by a representation of the SO(2,1)
Lorentz group. We then demonstrate how the holographic principle works for this
case, by constructing the operators corresponding to a field in space-time. The
parameter t turns out to be quantized in Planckian units, divided by the period
R of the compactified dimension.Comment: 12 pages plain tex, 1 figur

### Geometry of Scattering at Planckian Energies

We present an alternative derivation and geometrical formulation of Verlinde
topological field theory, which may describe scattering at center of mass
energies comparable or larger than the Planck energy. A consistent trunckation
of 3+1 dimensional Einstein action is performed using the standard geometrical
objects, like tetrads and spin connections. The resulting topological invariant
is given in terms of differential forms.Comment: 8

### Winding Solutions for the two Particle System in 2+1 Gravity

Using a PASCAL program to follow the evolution of two gravitating particles
in 2+1 dimensions we find solutions in which the particles wind around one
another indefinitely. As their center of mass moves `tachyonic' they form a
Gott-pair. To avoid unphysical boundary conditions we consider a large but
closed universe. After the particles have evolved for some time their momenta
have grown very large. In this limit we quantize the model and find that both
the relevant configuration variable and its conjugate momentum become discrete.Comment: 15 pages Latex, 4 eps figure

### Pauli-Lubanski scalar in the Polygon Approach to 2+1-Dimensional Gravity

In this paper we derive an expression for the conserved Pauli-Lubanski scalar
in 't Hooft's polygon approach to 2+1-dimensional gravity coupled to point
particles. We find that it is represented by an extra spatial shift $\Delta$ in
addition to the usual identification rule (being a rotation over the cut). For
two particles this invariant is expressed in terms of 't Hooft's phase-space
variables and we check its classical limit.Comment: Some errors are corrected and a new introduction and discussion are
added. 6 pages Latex, 4 eps-figure

### The mathematical basis for deterministic quantum mechanics

If there exists a classical, i.e. deterministic theory underlying quantum
mechanics, an explanation must be found of the fact that the Hamiltonian, which
is defined to be the operator that generates evolution in time, is bounded from
below. The mechanism that can produce exactly such a constraint is identified
in this paper. It is the fact that not all classical data are registered in the
quantum description. Large sets of values of these data are assumed to be
indistinguishable, forming equivalence classes. It is argued that this should
be attributed to information loss, such as what one might suspect to happen
during the formation and annihilation of virtual black holes.
The nature of the equivalence classes is further elucidated, as it follows
from the positivity of the Hamiltonian. Our world is assumed to consist of a
very large number of subsystems that may be regarded as approximately
independent, or weakly interacting with one another. As long as two (or more)
sectors of our world are treated as being independent, they all must be
demanded to be restricted to positive energy states only. What follows from
these considerations is a unique definition of energy in the quantum system in
terms of the periodicity of the limit cycles of the deterministic model.Comment: 17 pages, 3 figures. Minor corrections, comments and explanations
adde

### Are magnetic monopoles hadrons?

The charges of magnetic monopoles are constrained to a multiple of $2\pi$
times the inverse of the elementary unit electric charge. In the standard
model, quarks have fractional charge, raising the question of whether the basic
magnetic monople unit is a multiple of $2 \pi/e$ or three times that. A simple
lattice construction shows how a magnetic monopole of the lower strength is
possible if it interacts with gluonic fields as well. Such a monopole is thus a
hadron. This is consistent with the construction of magnetic monopoles in grand
unified theories.Comment: Poster presented at Lattice2004(topology), Fermilab, June 21-26,
2004. 3 pages, 5 figure

### Heavy meson semileptonic decays in two dimensions in the large Nc

We study QCD in 1+1 dimensions in the large Nc limit using light-front
Hamiltonian perturbation theory in the 1/Nc expansion. We use this formalism to
exactly compute hadronic transition matrix elements for arbitrary currents at
leading order in 1/Nc, which we use to write the semileptonic differential
decay rate of a heavy meson and its moments. We then compare with the results
obtained using an effective field theory approach based on perturbative
factorization, with the intention of better understanding quark-hadron duality.
A very good numerical agreement is obtained between the exact result and the
result using effective theories.Comment: Talk given at the High-Energy Physics International Conference on
Quantum Chromodynamics, 3-7 July (2006), Montpellier (France

### Towards a Simulation of Quantum Computers by Classical Systems

We present a two-dimensional classical stochastic differential equation for a
displacement field of a point particle in two dimensions and show that its
components define real and imaginary parts of a complex field satisfying the
Schroedinger equation of a harmonic oscillator. In this way we derive the
discrete oscillator spectrum from classical dynamics. The model is then
generalized to an arbitrary potential. This opens up the possibility of
efficiently simulating quantum computers with the help of classical systems.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re324/preprint.htm

### Chiral Anomaly and Index Theorem on a finite lattice

The condition for a lattice Dirac operator D to reproduce correct chiral
anomaly at each site of a finite lattice for smooth background gauge fields is
that D possesses exact zero modes satisfying the Atiyah-Singer index theorem.
This is also the necessary condition for D to have correct fermion determinant
(ratio) which plays the important role of incorporating dynamical fermions in
the functional integral.Comment: LATTICE99(chiral fermion), 3 pages, Latex, espcrc2.st

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